computer freezing in xp32 & xp 64 - won't boot xp32 safe mode!

My good ladies PC has started freezing up usually just after the desktop has loaded up, but only occasionaly when it will do it a few times in a row then be OK for a while. It is running AVG antivirus 7.5, Kaspersky anti-virus 7 plus spyware doctor, so I'm ruling out spyware/virus/trojans for the mo!)
so, specs:
AMD athlon 3400+ (2200MHZ) 64bit processor
K8M800 Mobo
1GB ram
160GB SATA Maxtor hard drive
NVIDIA GForce4 MX440 graphics card.

The problem has appeared recently, without any changes being made to hardware. The other day the system shut down as if power had been switched off, yet power was coming through as Monitor is running through the power supply.
It will boot fine in xp64 safe mode, yet in xp32 safe mode it freezes at the dreaded ACPITABL.DAT file, suggesting memory issues. Where should I start??????
Do you reckon it's memory, power supply or both?